by Cauchy logic and economics [embedded content] Yours truly has no problem with solving problems in mathematics by ‘defining’ them away. But how about the real world? Maybe that ought to be a question to ponder even for economists all to fond of uncritically following the mathematical way when applying their mathematical models to the real world, where indeed “you can never have infinitely many heaps” … In econometrics we often run into the ‘Cauchy logic’ — the data is treated as if it were from a larger population, a ‘superpopulation’ where repeated realizations of the data are imagined. Just imagine there could be more worlds than the one we live in and the problem is fixed … Accepting Haavelmo’s domain of probability theory and sample space of infinite
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Cauchy logic and economics
Yours truly has no problem with solving problems in mathematics by ‘defining’ them away. But how about the real world? Maybe that ought to be a question to ponder even for economists all to fond of uncritically following the mathematical way when applying their mathematical models to the real world, where indeed “you can never have infinitely many heaps” …
In econometrics we often run into the ‘Cauchy logic’ — the data is treated as if it were from a larger population, a ‘superpopulation’ where repeated realizations of the data are imagined. Just imagine there could be more worlds than the one we live in and the problem is fixed …
Accepting Haavelmo’s domain of probability theory and sample space of infinite populations – just as Fisher’s “hypothetical infinite population, of which the actual data are regarded as constituting a random sample”, von Mises’s “collective” or Gibbs’s ”ensemble” – also implies that judgments are made on the basis of observations that are actually never made!
Infinitely repeated trials or samplings never take place in the real world. So that cannot be a sound inductive basis for a science with aspirations of explaining real-world socio-economic processes, structures or events. It’s — just as the Cauchy mathematical logic of ‘defining’ away problems — not tenable.
In social sciences — including economics — it’s always wise to ponder C. S. Peirce’s remark that universes are not as common as peanuts …